In the end, China’s leadership has calculated that it must try to rise above what it considers a struggle between two tired powers and be seen as a pillar of stability in an increasingly turbulent world.

“This means that as long as we don’t commit terminal strategic blunders, China’s modernization will not be cut short, and on the contrary, China will have even greater ability and will to play a more important role in building a new international order,” Zheng Yongnian, a professor at the Chinese University of Hong Kong, Shenzhen, who has advised senior officials, wrote after the invasion in a widely circulated article.

At the heart of China’s strategy lies a conviction that the United States is weakened from reckless foreign adventures, including, from Beijing’s perspective, goading Mr. Putin into the Ukraine conflict.

In this view, which in recent days has been echoed in public statements and quasi-official analyses, Russia’s invasion has dragged American power and attention toward Europe, making it likely that President Biden, like his recent predecessors, will try but fail to put more focus on China and the broader Asia-Pacific region.